8 ideas
| 13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
| Full Idea: Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects. | |
| From: comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414 | |
| A reaction: This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear. |
| 12219 | Whether a modal claim is true depends on how the object is described [Quine, by Fine,K] |
| Full Idea: Quine says if ∃x□(x>7) makes sense, then for which object x is the condition rendered true? Specify it as '9' and it is apparently rendered true, specify it as 'the number of planets' and it is apparently rendered false. | |
| From: report of Willard Quine (Three Grades of Modal Involvement [1953]) by Kit Fine - Quine on Quantifying In p.105 | |
| A reaction: This is normally characterised as Quine saying that only de dicto involvement is possible, and not de re involvement. Or that that all essences are nominal, and cannot be real. |
| 13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
| Full Idea: In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments. | |
| From: Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3 | |
| A reaction: This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view. |
| 10922 | Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine] |
| Full Idea: The objects of a theory are not properly describable as the things named by the singular terms; they are the values, rather, of the variables of quantification. ..So a referentially opaque context is one that cannot properly be quantified into. | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.174) | |
| A reaction: The point being that you cannot accurately pick out the objects in the domain |
| 10923 | Aristotelian essentialism says a thing has some necessary and some non-necessary properties [Quine] |
| Full Idea: What Aristotelian essentialism says is that you can have open sentences Fx and Gx, such that ∃x(nec Fx.Gx.Źnec Gx). For example, ∃x(nec(x>5). there are just x planets. Źnec(there are just x planets)). | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.176) | |
| A reaction: This is a denial of 'maximal essentialism', that all of a things properties might be essential. Quine is thus denying necessity, except under a description. He may be equivocating over the reference of 'there are just 9 planets'. |
| 10921 | Necessity can attach to statement-names, to statements, and to open sentences [Quine] |
| Full Idea: Three degrees necessity in logic or semantics: first and least is attaching a semantical predicate to the names of statements (as Nec '9>5'); second and more drastic attaches to statements themselves; third and gravest attaches to open sentences. | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.158) |
| 10924 | Necessity is in the way in which we say things, and not things themselves [Quine] |
| Full Idea: Necessity resides in the way in which we say things, and not in the things we talk about. | |
| From: Willard Quine (Three Grades of Modal Involvement [1953], p.176) | |
| A reaction: This is a culminating idea of Quine's thoroughgoing empiricism, as filtered through logical positivism. I would hardly dare to accuse Quine of a use/mention confusion (his own bęte noir), but one seems to me to be lurking here. |
| 7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
| Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
| From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
| A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |